Privacy preserving query transformation and processing in location based service

PRIVACY-PRESERVING QUERY TRANSFORMATION AND PROCESSING IN LOCATION BASED SERVICES GABRIEL GHINITA A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF COMPUTER SCIENCE NATIONAL UNIVERSITY OF SINGAPORE 2008 Abstract The increasing trend of embedding positioning capabilities (e.g., GPS) in mobile devices has created unprecedented opportunities for the widespread use of Location Based Services (LBS). Mobile users are able to formulate spatial queries, such as “find the closest restaurant to my current position”. For such applications to succeed, privacy and confidentiality are essential. Commonly, privacy-enhancing techniques rely on encryption to safeguard communication channels, and on pseudonyms to protect user identities. Nevertheless, an LBS query contains the current location of the user, which may be mapped to the user’s identity through a variety of means, such as signal triangulation, or physical observation. Hiding the user location is a challenging task, and a primordial requirement for LBS privacy. This thesis presents a framework for private queries in location-based services. First, we study in depth the location privacy problem in the context of spatial K-anonymity (SKA), an extension of the K-anonymity paradigm, widely used for privacy preservation in relational databases. To enforce SKA, we adopt a three-tier architecture, with an Anonymizer Service (AS) that acts as an intermediary between the users and the LBS, and anonymizes queries by cloaking user locations. We identify the reciprocity property, a sufficient condition to guarantee privacy for a snapshot of user locations, and develop two SKA algorithms which provide a trade-off between privacy requirements and query processing overhead. We also devise algorithms to process range and nearest-neighbor anonymized queries at the LBS side. Next, we extend our results by showing how reciprocity can be effectively and efficiently enforced using hierarchical spatial indices, such as Quad-trees and R-trees. We also develop a stronger version of reciprocity - frequencyaware reciprocity - which addresses the scenario when an attacker possesses additional background knowledge about the relative frequencies of issuing queries among distinct users. Most existing work in LBS query privacy assumes a centralized AS, which must handle the frequent updates of user locations, as well as the overhead of anonymizing queries. Furthermore, the AS is a single-point-of-attack, and, if compromised, the privacy of all users is threatened. We address these limitations by devising a decentralized architecture for LBS anonymization: users organize themselves into a P2P network, and cooperate to anonymize queries. We propose two such P2P systems, which provide a trade-off between privacy requirements and scalability. Finally, we take a step further from the SKA paradigm, and propose a novel LBS privacy approach, based on Private Information Retrieval (PIR). PIR comprises of a two-party cryptography-based protocol that allows a client to retrieve the desired information from a server, without the server learning what information was requested. We show that PIR eliminates the need to trust a third-party anonymizer, as well as other users. Furthermore, since location information is encrypted (not just cloaked, as in the case of spatial K -anonymity), this method is resilient to any type of location-based attack. For instance, PIR-based privacy protects against correlation attacks in the case of private continuous queries (i.e., a user asks the same query from different locations at consecutive timestamps), a problem which has not been efficiently solved yet within the SKA paradigm. The PIR approach provides superior privacy, and incurs a reasonable overhead in practice. Acknowledgments I would like to thank my supervisor, Dr. Panos Kalnis, for his guidance and support throughout my Ph.D. studies. I would also like to thank the members of my examination committee for their interest and time spent on this PhD dissertation: Dr. Li Mong Lee and Dr. Chee Yong Chan from National University of Singapore, and Dr. George Kollios (external reviewer) from Boston University. I am also grateful for their support and advice, as well as the numerous interesting research discussions, which represented the source of valuable ideas, to: Dr. Dimitris Papadias (Hong Kong University of Science and Technology), Dr. Nikos Mamoulis (Hong Kong University), Dr. Kian-Lee Tan (National University of Singapore), Dr. Yufei Tao (Chinese University of Hong Kong), Dr. Cyrus Shahabi (University of Southern California), Dr. Kyriakos Mouratidis (Singapore Management University), Dr. Panagiotis Karras (University of Zurich), Dr. Spiros Skiadopoulos (University of Peloponnese), Dr. Man Lung Yiu (Aalborg University) and Mr. Xiaokui Xiao (Chinese University of Hong Kong). i Contents Introduction 1.1 Contributions and Thesis Organization . . . . . . . . . . . . . Related Work 10 2.1 K-anonymity . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Spatial K -anonymity. Assumptions and Goals . . . . . . . . . 12 2.3 Existing SKA Techniques . . . . . . . . . . . . . . . . . . . . 16 2.4 Related Spatial Query Processing Techniques . . . . . . . . . 21 2.5 Related P2P Systems . . . . . . . . . . . . . . . . . . . . . . . 23 2.6 Private Information Retrieval . . . . . . . . . . . . . . . . . . 24 SKA Framework for LBS Privacy 26 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2 Nearest Neighbor Cloak . . . . . . . . . . . . . . . . . . . . . 27 3.3 Reciprocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4 Hilbert Cloak . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.5 Location-Based Service Query Processing . . . . . . . . . . . 32 3.5.1 CkNN - Circular Range kNN . . . . . . . . . . . . . . 32 3.5.2 R-trees and CkNN . . . . . . . . . . . . . . . . . . . . 35 Experimental Evaluation . . . . . . . . . . . . . . . . . . . . . 40 3.6.1 Anonymizer Evaluation . . . . . . . . . . . . . . . . . 40 3.6.2 Location-Based Service Evaluation . . . . . . . . . . . 44 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.6 3.7 Reciprocal Framework for SKA 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii 52 52 4.2 Algorithm for Reciprocal Cloaking . . . . . . . . . . . . . . . 52 4.3 Partitioning Methods . . . . . . . . . . . . . . . . . . . . . . . 57 4.3.1 Greedy Hilbert Partitioning (GH) . . . . . . . . . . . 57 4.3.2 Asymmetric R-tree Split (AR) . . . . . . . . . . . . . 62 4.3.3 Dynamic Programming Hilbert (DH) . . . . . . . . . . 64 4.3.4 Top-Down Clustering (TD) . . . . . . . . . . . . . . . 66 4.3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.4 SKA With Variable Query Frequencies . . . . . . . . . . . . . 67 4.5 Experimental Evaluation . . . . . . . . . . . . . . . . . . . . . 70 4.5.1 Evaluation of Partitioning Techniques . . . . . . . . . 70 4.5.2 Comparison with Hilbert Cloak (HC) . . . . . . . . . 76 4.5.3 Variable Query Frequencies . . . . . . . . . . . . . . . 77 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.6 Decentralized Query Anonymization 80 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.2 ´ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prive 81 5.3 5.4 5.5 B+ -tree 5.2.1 Hilbert Cloak with a index . . . . . . . . . . . 83 5.2.2 Protocol Overview . . . . . . . . . . . . . . . . . . . . 84 5.2.3 Protocol Operations . . . . . . . . . . . . . . . . . . . 86 5.2.4 Fault Tolerance and Load Balancing . . . . . . . . . . 89 MobiHide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.3.1 The Correlation Attack . . . . . . . . . . . . . . . . . 94 5.3.2 Protocol Overview . . . . . . . . . . . . . . . . . . . . 95 5.3.3 Protocol Operations . . . . . . . . . . . . . . . . . . . 97 5.3.4 Fault-tolerance and Load Balancing . . . . . . . . . . 99 Experimental Evaluation . . . . . . . . . . . . . . . . . . . . . 102 5.4.1 ´ protocol . . . . . . . . . . . . . . . . . . . . . . 103 Prive 5.4.2 MobiHide protocol . . . . . . . . . . . . . . . . . . . 111 5.4.3 ´ and MobiHide Comparison . . . . . . . . . . . 114 Prive Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 PIR Framework for LBS 6.1 120 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 iii 6.2 Computational PIR Protocol . . . . . . . . . . . . . . . . . . 121 6.3 PIR and Location-dependent Queries . . . . . . . . . . . . . . 124 6.4 Approximate Nearest Neighbors . . . . . . . . . . . . . . . . . 125 6.5 6.4.1 Approximate NN using Hilbert ordering . . . . . . . . 125 6.4.2 Generalization to 2-D partitionings . . . . . . . . . . . 128 Exact Nearest Neighbors . . . . . . . . . . . . . . . . . . . . . 129 6.5.1 6.6 6.7 6.8 Grid Granularity . . . . . . . . . . . . . . . . . . . . . 132 Optimizations . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.6.1 Compression . . . . . . . . . . . . . . . . . . . . . . . 133 6.6.2 Rectangular vs. Square PIR Matrix . . . . . . . . . . 133 6.6.3 Avoiding Redundant Multiplications . . . . . . . . . . 135 6.6.4 Parallelism . . . . . . . . . . . . . . . . . . . . . . . . 138 Experimental Evaluation . . . . . . . . . . . . . . . . . . . . . 138 6.7.1 1D and 2D Approximate NN . . . . . . . . . . . . . . 139 6.7.2 Exact Methods . . . . . . . . . . . . . . . . . . . . . . 141 6.7.3 Execution Time Optimizations . . . . . . . . . . . . . 143 6.7.4 User CPU Time . . . . . . . . . . . . . . . . . . . . . 144 6.7.5 PIR vs. Anonymizer-based Methods . . . . . . . . . . 144 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Conclusions and Future Work 148 7.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . 148 7.2 Directions for Future Research . . . . . . . . . . . . . . . . . 150 A Analysis of Privacy in Casper and Interval Cloak iv 159 List of Tables 5.1 ´ Protocol Terminology . . . . . . . . . . . . . . . . . . Prive 6.1 Summary of notations . . . . . . . . . . . . . . . . . . . . . . 121 6.2 Grid Granularity for ExactNN . . . . . . . . . . . . . . . . . 141 v 86 List of Figures 1.1 Hiding identity with pseudonyms is not sufficient . . . . . . . 1.2 Example: “Find the nearest hospital”. . . . . . . . . . . . . . 1.3 Framework for Spatial K -anonymity (SKA) . . . . . . . . . . 1.4 PIR framework . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Thesis Roadmap . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Distance from MBR center for Center Cloak (K =10) . . . . . 15 2.2 Example of Interval Cloak and Casper . . . . . . . . . . . . . 17 2.3 Location anonymity compromise in the presence of outliers . 19 2.4 Example of Clique Cloak . . . . . . . . . . . . . . . . . . . . . 19 2.5 Example of continuous NN search . . . . . . . . . . . . . . . . 22 3.1 Example of NNC . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 K -ASR Reciprocity Example, K =5 . . . . . . . . . . . . . . . 28 3.3 Hilbert Curve (left: × 4, right: × 8) . . . . . . . . . . . . . 30 3.4 Example of Hilbert Cloak . . . . . . . . . . . . . . . . . . . . 31 3.5 The 1-NNs of C are p1 and p2 . . . . . . . . . . . . . . . . . . 33 3.6 CkNN example: perpendicular bisector does not intersect C . 34 3.7 The perpendicular bisector intersects C . . . . . . . . . . . . . 35 3.8 Find the 1-NNs of a circular range C . . . . . . . . . . . . . . 36 3.9 Check if E may contain qualifying objects . . . . . . . . . . . 37 3.10 The M BR and the M ER of C . . . . . . . . . . . . . . . . . 38 3.11 North-America (NA) dataset . . . . . . . . . . . . . . . . . . 40 3.12 Area of rectangular K -ASR . . . . . . . . . . . . . . . . . . . 41 3.13 K -ASR generation time . . . . . . . . . . . . . . . . . . . . . 42 3.14 Rectangular vs SA K -ASR, Nearest Neighbor Cloak 43 vi . . . . . 3.15 center-of-ASR attack, K = 50 . . . . . . . . . . . . . . . . . . 44 3.16 kNN queries, varying k, N = 50, 000, K = 80 . . . . . . . . . 45 3.17 kNN queries, varying K , k = neighbors, N = 50, 000 . . . . 46 3.18 kNN queries, varying N , k = 2, K = 80 . . . . . . . . . . . . 47 3.19 Range queries, N = 50, 000, varying K . . . . . . . . . . . . . 48 3.20 NNC , rectangular vs SA K -ASR, k = 2, N = 50, 000 . . . . . 49 3.21 NNC , rectangular vs SA K -ASR, k = 2, K = 80 . . . . . . . 50 4.1 Reciprocal Cloaking . . . . . . . . . . . . . . . . . . . . . . . 53 4.2 Partitioning with a Quad-tree . . . . . . . . . . . . . . . . . . 55 4.3 GH partitioning for (leaf) level . . . . . . . . . . . . . . . . 58 4.4 GH partitioning for level . . . . . . . . . . . . . . . . . . . . 59 4.5 Greedy Hilbert - general method . . . . . . . . . . . . . . . . 61 4.6 R*-tree split vs AR . . . . . . . . . . . . . . . . . . . . . . . . 63 4.7 Asymmetric R-tree Split (AR) . . . . . . . . . . . . . . . . . 64 4.8 GH and DH partitions for K=4 . . . . . . . . . . . . . . . . . 65 4.9 Reciprocal Cloaking Change for Variable Frequency . . . . . 68 4.10 FQGH partitioning, K=2 . . . . . . . . . . . . . . . . . . . . 69 4.11 R-tree Cloak (RC). Partitioning methods versus K . . . . . . 71 4.12 Quad-tree Cloak (QC). Partitioning methods versus K . . . . 72 4.13 RC versus page size . . . . . . . . . . . . . . . . . . . . . . . 73 4.14 QC versus page size . . . . . . . . . . . . . . . . . . . . . . . 74 4.15 RC-GH and RC-AR versus HC . . . . . . . . . . . . . . . . . 76 4.16 P N overhead for variable query frequency . . . . . . . . . . . 77 4.17 RC-FQGH versus HCf . . . . . . . . . . . . . . . . . . . . . . 78 ´ . . . . . . . . . . . . . . . . . . . . . . Architecture of Prive 82 5.1 B+ -tree 5.2 Hilbert Cloak with Annotated . . . . . . . . . . . . . 84 5.3 Distributed Index Structure, α=2 . . . . . . . . . . . . . . . . 85 5.4 User Join and Relocation, α=2 . . . . . . . . . . . . . . . . . 87 5.5 User Relocation Pseudocode . . . . . . . . . . . . . . . . . . . 88 5.6 K -request, α=2, K =6 . . . . . . . . . . . . . . . . . . . . . . 89 5.7 K -request . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.8 Load Balancing Mechanism . . . . . . . . . . . . . . . . . . . 91 vii putational cost incurred by PIR may be high in comparison with SKA. For this purpose, we plan to study in future work methods to further reduce the computational overhead of PIR. 147 Chapter Conclusions and Future Work 7.1 Summary of Contributions This thesis has focused on a comprehensive framework for private queries in Location Based Services (LBS). We have identified the main objectives and assumptions behind LBS query privacy, and we have systematically built solutions that address the limitations of existing techniques. In summary, our contributions are: Secure SKA Algorithms. We have first considered the already established setting in most existing work, i.e. Spatial K-anonymity (SKA) within a centralized Anonymizer Server (AS) architecture. In Chapter 3, we have identified the reciprocity property, a sufficient condition to guarantee SKA for a snapshot of user locations. Our work was the first to provide privacy guarantees in the above-mentioned setting. We have proposed two SKA algorithms: Nearest Neighbor Cloak and Hilbert Cloak . Nearest Neighbor Cloak uses a randomized variation of NN search, and significantly outperforms existing techniques in terms of K -ASR size, by a factor of up to times. Hilbert Cloak builds upon the reciprocity property, and provides provable privacy guarantees, independently of the user location distribution. Anonymized Query Processing at LBS. The LBS overhead incurred by the processing of anonymized queries is an important concern. In Chap- 148 ter 3, we have introduced a novel algorithm for finding the NN of a circular region, as opposed to rectangular regions which were considered previously. We have shown that by using circular ASRs, the LBS overhead can be reduced by a significant margin. SKA Reciprocity with Variable Query Frequency. We have also considered the scenario in which a determined attacker has additional background knowledge on the query frequency of various users. In Chapter 4, we extended the reciprocity property to account for differences in probability of issuing a query at distinct users. Reciprocal Framework for SKA. In Chapter we have introduced a methodology for building reciprocal ASRs in a systematic manner. We have proposed a family of partitioning methods based on hierarchical spatial indices, with various trade-offs between ASR size and generation time. The reciprocal framework also addresses the variable query frequency setting. Our AR partitioning method outperforms existing solutions by a factor of in terms of ASR size, while the proposed GH method (and its frequency-aware counterpart) incurs an ASR generation time up to an order of magnitude lower than competitor methods. Decentralized LBS Query Anonymization. Motivated by the limitations of the centralized AS architecture, we have considered in Chapter a distributed architecture for LBS query anonymization. Users self-organize in a P2P overlay network, and cooperate to anonymize queries. We pro´ and MobiHide, which provide a posed two different P2P protocols, Prive ´ implements trade-off between privacy guarantees and response time. Prive the Hilbert Cloak algorithm in a distributed fashion and offers privacy guarantees. MobiHide relies on a randomized version of Hilbert Cloak , which allows a fully-decentralized implementation on top of the Chord [57] DHT. MobiHide guarantees privacy for uniform query distribution, and offers excellent scalability with the number of subscribed users, with a response time of under seconds in the worst case. PIR-based LBS Privacy. Finally, in Chapter 6, we proposed a completely novel approach to LBS privacy, based on Private Information Retrieval (PIR). This approach has several fundamental advantages over its SKA-based counterparts: specifically, (i) it offers strong privacy guarantees, 149 that not depend on the existence of a large number of trusted thirdparties, in the form of the AS and its subscribed users. (ii) it eliminates the need for the maintenance of locations for a large population of mobile users and (iii) it thwarts any type of location-based attack, as it does not disclose any location information whatsoever to the LBS server (not even in perturbed form). We have also shown the benefits of PIR techniques in terms of commercial considerations: the number of points of interest disclosed, which is a good estimator of the financial cost incurred by LBS users, is one order of magnitude smaller for PIR than for SKA-based techniques. 7.2 Directions for Future Research We envision extending this research along the following directions: • A challenging problem is to ensure anonymity for users issuing continuous spatial queries. Intuitively, preserving anonymity is more difficult in this case: asking the same query from successive locations may disclose the identity of the querying user, who will be included in all ASRs. Although we have addressed this problem with our PIR approach, the issue remains open under the SKA paradigm. Our SKA methods can be extended for processing continuous queries as follows: a snapshot technique (e.g., NNC, HC ) is first employed to determine the set AS of users included in the ASR for the initial snapshot of the query; this anonymizing set is “frozen” for the rest of the query lifetime. The MBR of AS is then used as ASR at subsequent snapshots1 . However, as users move in different directions, such an approach may yield large ASRs. Furthermore, if one of the users in AS disconnects, it compromises the privacy of the other users. Continuous queries involve several complex issues, and constitute a promising topic for further work. • Another interesting aspect to enhance the privacy offered by SKA methods is preventing “background knowledge” attacks, when the attacker has additional information about the preferences of certain Such an approach has been proposed in [20], as discussed in Chapter 2. 150 users. For instance, if Bob, a rugby fan, asks for the location of the closest rugby club, and the associated ASR contains only female users in addition to Bob, the attacker may infer Bob as query source with higher probability. A solution to this problem would be to group users into partitions according to their areas of interest (e.g., users who query frequently about restaurants, or night clubs, etc). Then, when a query is issued, the corresponding ASR is generated with users from the same interest group as the query source, such that each user in the ASR has an equally likely probability of having asked the query. • Our P2P anonymization methods currently assume a communication network infrastructure (such as IP connectivity), where users can establish point-to-point connections. An interesting direction for future work is to devise protocols for infrastructure-less networks, in which only mobile devices within communication range can connect to each other (for instance, using Wi-Fi or Bluetooth connections). Furthermore, it would be interesting to develop real-life prototypes of the proposed decentralized anonymization systems, in order to confirm their feasibility in practice. • Although it offers much stronger privacy guarantees, and works under more relaxed assumptions than SKA, our PIR LBS privacy approach may incur increased computational and communication cost. 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In Proc. of ICDE, 2007. 158 Appendix A Analysis of Privacy in Casper and Interval Cloak Among the systems reviewed in Section 2.2, Casper and Interval Cloak perform spatial cloaking, using the same architecture and following the same assumptions as our techniques. Next, we show formally that both approaches are not secure. Recall that the shape of an ASR in Casper can be either a square, or the horizontal/vertical union of two adjacent cells under the same parent. We first analyze the case of square ASRs assuming that an attacker detects the ASR of Figure A.1a. Then, s/he can infer that it was created due to a query from a user U in A, B, C, D. If U is in cell A, the required degree of anonymity KA must be in the range [MA + 1, |A| + |B| + |C| + |D|]. MA = |A| + max{|B|, |C|} is due to the fact that neither A ∪ B, nor A ∪ C contains sufficient points (otherwise the ASR would be A ∪ B, or A ∪ C). Similar to KA , we can calculate the ranges of KB , KC and KD which have the same maximum value |A| + |B| + |C| + |D|, but different lower bounds MB = |B| + max{|A|, |D|}, MC = |C| + max{|A|, |D|} and MD = |D| + max{|B|, |C|}, respectively. Summarizing, the ASR is generated by a query originating from (i) A with anonymity KA , i.e., |A| · (|A| + |B| + |C| + |D| − MA ) events, or (ii) B with KB , i.e., |B| · (|A| + |B| + |C| + |D| − MB ) events, or (iii) C with KC , i.e., |C| · (|A| + |B| + |C| + |D| − MC ) events, or (iv) D with KD , i.e., |D| · (|A| + |B| + |C| + |D| − MD ) events. The total number of events is 159 (|A| + |B| + |C| + |D|)/2 − |A| · MA − |B| · MB − |C| · MC − |D| · MD . Given no additional knowledge about the query frequency and the anonymity degree distributions, the attacker considers that these events have equal probabilities. For instance, s/he assumes that the query originates from A with probability: PA = |A| · (|A| + |B| + |C| + |D| − MA ) (|A| + |B| + |C| + |D|)2 − |A| · MA − |B| · MB − |C| · MC − |B| · MD (A.1) Within A, each individual user can issue the query with equal probability PA /|A|. For SKA to be preserved, it must hold that PA /|A| ≤ 1/KA . Since the maximum value of KA is |A| + |B| + |C| + |D|, we have PA /|A| ≤ 1/(|A|+|B|+|C|+|D|). Applying the same reasoning to PB /|B|, PC /|C| and PD /|D| and some algebraic simplifications, we derive the following system of linear inequalities: |B| · MB + |C| · MC + |D| · MD |B| + |C| + |D| |A| · MA + |C| · MC + |D| · MD MB = |A| + |C| + |D| |A| · MA + |B| · MB + |D| · MD MC = |A| + |B| + |D| |A| · MA + |B| · MB + |C| · MC MD = |A| + |B| + |C| MA = (A.2) (A.3) (A.4) (A.5) The solution to the above system has the only form MA = MB = MC = MD . MA = MD implies that |A| = |D|, and MB = MC that |B| = |C|. In other words, each pair of diagonal cells should have the same cardinality; otherwise Casper fails to preserve SKA. As an example consider Figure A.1a, where A, C and D contain one user each, and B includes 10 users (MA = MB = MD = 11, MC = 2). Assuming that the query originates from UC in cell C, then KC must be in the range [3, 13]. The attacker will infer UC as the origin with probability PC /|C| = 11/35, which exceeds 1/KC for KC ≥ 4. Thus, the anonymity of UC is breached for all, but one, queries involving this ASR. Having established that the diagonal neighbors must have the same cardinality (in order not to compromise square ASRs), we will show that the horizontal (and vertical) neighbors must also satisfy the same condition. 160 UA A UC B A D C ASR B ASR C (a) Square ASR D (b) 2x1 Rectangular ASR Figure A.1: Examples of Casper ASRs Assume a rectangular ASR consisting of cells A and B as shown in Figure A.1b. Clearly, the query may have originated from a user U in A or B. If U is in A, the required degree of anonymity KA must be in the range [|A| + 1, |A| + |B|]. This is because if KA ≤ |A|, the ASR would not include B (as the points in A would suffice). Otherwise, if KA > |A| + |B|, the ASR should be larger than the union of A and B. Similarly, if the query is issued by any user from B, the degree of anonymity KB is in the range [|B| + 1, |A| + |B|]. The ASR is generated by (i) a query originating from A with KA , i.e., |A|·|B| events, or (ii) a query originating from B with KB , i.e., |B|·|A| events. Given that these events have equal probabilities, the attacker assumes that the query originates from A or B with PA = PB = |A| · |B|/(2 · |A| · |B|) = 1/2. Within A or B, each individual user can issue the query with equal probability PA /|A| = 1/(2 · |A|) or PB /|B| = 1/(2 · |B|), respectively. SKA requires that PA /|A| ≤ 1/KA and PB /|B| ≤ 1/KB . Because the maximum value of KA and KB is |A|+|B|, it must hold that 1/(2·|A|) ≤ 1/(|A|+|B|), and 1/(2 · |B|) ≤ 1/(|A| + |B|), which are simultaneously satisfied only when |A| = |B|. In case that |A| = |B|, Casper fails to preserve SKA. For instance, in Figure A.1b (|A| = |D| = 5, |B| = |C| = 10), assume that the ASR is generated due to a query from UA with KA in [6, 15]. The attacker will pinpoint UA with probability PA /|A| = 1/10, which compromises anonymity for all values of KA in the range [11, 15]. In conclusion, Casper achieves SKA only when each cell (at any level) contains exactly the same number of users as its neighbors, i.e., only for perfectly uniform user distribution. The analysis of Interval Cloak is similar 161 to Casper; except that (i) the ASR is always square, and (ii) MA = |A|, MB = |B|, MC = |C| and MD = |D|, because if a cell does not contain enough users, the method uses directly its parent. Thus, the previous system of inequalities implies that in order to guarantee anonymity, it should hold that |A| = |B| = |C| = |D|, meaning that Interval Cloak is also applicable only to uniform datasets. 162 [...]... for three points of interest stored at the LBS, denoted by p1 p3 The initial set of candidates contains all points (p1 , p2 ) inside the input range (i.e., the ASR) Then, four continuous NN (CNN) queries [60], one for each side of the ASR, retrieve the remaining candidates Consider, for instance, the CNN query for the bottom side se The initial candidates split se into two intervals: ss1 and s1 e,... inside some vicinity circle Continuing the example, p3 falls inside the last two vicinity circles and updates the result as shown in Figure 2.5b Specifically, s1 is the point where the perpendicular bisector of p1 p3 intersects se: p1 becomes the NN of every point in ss1 , and p3 the NN of every point in s1 e Note that the vicinity circles shrink as new data points are discovered The process terminates 22... incur high information loss in practice Finally, Xiao and Tao [65] have proposed m-invariance, a privacy model for publishing sequential data releases 2.2 Spatial K -anonymity Assumptions and Goals In the LBS domain, K -anonymity was first introduced in [33] Spatial K anonymity (SKA) prevents an attacker from learning exact user locations Given a query from user u, SKA techniques replace the exact location. .. locations 2.4 Related Spatial Query Processing Techniques The LBS maintains the locations of points-of-interest and answers cloaked queries The most common spatial queries, and the focus of the existing systems, are ranges and nearest neighbors (NN) While the cloaking mechanism at the anonymizer is independent of the query type, query processing at the LBS depends on the query Range queries are usually straightforward;... Bob uses his phone within his residence, Eve can easily convert the coordinates to a street address (most on-line maps provide this service) and relate the address to Bob by accessing an on-line white pages service A broad discussion on the risks of revealing sensitive information in location- based services can be found in [16] In practice, users would be reluctant to access a service that may disclose... quality of service (QoS), i.e., some queries must be delayed or dropped, in order to preserve user privacy (iii) They are ineffective, i.e., they generate large ASRs, resulting in high query processing cost, and increased communication to transfer a large number of candidate results from the LBS back to the AS (iv) They focus exclusively on cloaking mechanisms, and lack algorithms for query processing at... learning anything about B and vice versa They encrypt their objects using random keys and follow a protocol, which results into two “shares” SA and SB given to A and B, respectively By combining their shares, they compute the value of f In contrast to our problem (which hides the querying user from the LBS), existing NN techniques assume that the query is public, whereas the database is partitioned into... Cloaking [18] preserves the privacy of locations without applying spatial K -anonymity Instead, (i) the ASR is a closed region around the query point, which is independent of the number of users inside and (ii) the location of the query is uniformly distributed in the ASR Given an ASR, the LBS returns the probability that each candidate result satisfies the query, based on its location with respect to... background on the LBS query privacy problem, and surveys existing LBS privacy techniques In Section 2.1, we briefly discuss the K -anonymity paradigm in relational databases, while in 2.2 we present Spatial K -anonymity, and introduce its assumptions and objectives In Section 2.3, we survey existing SKA techniques, and highlight their limitations Section 2.4 focuses on processing of anonymized queries... guarantee query privacy for a snapshot of user locations Intuitively, reciprocity requires that whenever user ui includes uj in its corresponding ASR, uj also includes ui in its ASR when it issues a query We propose two cloaking algorithms: Nearest Neighbor Cloak and Hilbert Cloak Nearest Neighbor Cloak builds K -ASRs based on user proximity, and significantly outperforms existing techniques in terms . PRIVACY- PRESERVING QUERY TRANSFORMATION AND PROCESSING IN LOCATION BASED SERVICES GABRIEL GHINITA A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR. (most on-line maps provide this service) and relate the address to Bob by accessing an on-line white pages service. A broad discussion on the risks of revealing sensitive information in location- based. Hiding the user location is a challenging task, and a primordial requirement for LBS privacy. This thesis presents a framework for private queries in location- based services. First, we study in